Worksheet: Magnitude of a 2D Vector

In this worksheet, we will practice determining the magnitude of two-dimensional vectors.

Q1:

What is the magnitude of the vector 𝐴𝐵, where 𝐴=(5,9) and 𝐵=(9,1)?

  • A4
  • B 1 0
  • C 1 4
  • D116
  • E 2 2 9

Q2:

What is the magnitude of the vector 5,12?

Q3:

Given that v=8,15, find the value of ||v.

Q4:

What is the magnitude of the vector 4,5?

  • A 4 1
  • B 4
  • C41
  • D 5
  • E1

Q5:

Given that v=3,1, find the value of ||v.

  • A2
  • B 3
  • C10
  • D 1
  • E 1 0

Q6:

Given that v=0.6,0.8, find the value of ||v.

Q7:

What is the magnitude of the vector 𝐴𝐵 where 𝐴=(11,3) and 𝐵=(7,3)?

Q8:

How do you write the magnitude of a vector v?

  • A m ( ) v
  • B m a g ( ) v
  • C [ ] v
  • D | | v
  • E ̂ v

Q9:

The vector v is shown on the grid of unit squares below. Find the value of ||v.

Q10:

The vector v is shown on the grid of unit squares below. Find the value of ||v.

Q11:

The vector v is shown on the grid of unit squares below. Find the value of ||v.

Q12:

What is the magnitude of the vector 𝐴𝐵, where 𝐴=(9,13) and 𝐵=(1,12)?

  • A10
  • B 3 1 1
  • C1
  • D 1 0 1
  • E101

Q13:

What is the magnitude of the vector 0,7?

Q14:

Given that A=2,14, find ||A.

  • A 1 0 2
  • B 3 2
  • C4
  • D200

Q15:

Given that Aij=53, where i and j are two perpendicular unit vectors, find ||A.

  • A 1 4
  • B 3 4
  • C 2 2
  • D 2 7

Q16:

What is the magnitude of the vector 3.2,12.6?

Q17:

Find the magnitude of the vector v shown on the grid of unit squares below.

Q18:

Find the magnitude of the vector v shown on the grid of unit squares below.

  • A 2 5
  • B50
  • C 5 2
  • D 1
  • E7

Q19:

Find the magnitude of the vector v shown on the grid of unit squares below.

Q20:

Consider the vectors u=2,3 and v=4,6.

What is the magnitude of u? Give your answer correct to two decimal places if needed.

What is the magnitude of v? Give your answer correct to two decimal places if needed.

What is the magnitude of uv+? Give your answer correct to two decimal places if needed.

Q21:

Given that v=3,0, find the value of ||v.

Q22:

The vector v is shown on the grid of unit squares below. Find the value of ||v.

  • A9
  • B5
  • C 5
  • D 3
  • E 2

Q23:

The vector v is shown on the grid of unit squares below. Find the value of ||v.

  • A13
  • B 2
  • C 1 3
  • D 3
  • E 5

Q24:

Find the magnitude of the vector v shown on the grid of unit squares below.

Q25:

The vector v is shown on the grid of unit squares below. Find the value of ||v.

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